Question: Solve for $t$, $ \dfrac{10}{3t + 12} = -\dfrac{5t - 5}{t + 4} - \dfrac{4}{5t + 20} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3t + 12$ $t + 4$ and $5t + 20$ The common denominator is $15t + 60$ To get $15t + 60$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{10}{3t + 12} \times \dfrac{5}{5} = \dfrac{50}{15t + 60} $ To get $15t + 60$ in the denominator of the second term, multiply it by $\frac{15}{15}$ $ -\dfrac{5t - 5}{t + 4} \times \dfrac{15}{15} = -\dfrac{75t - 75}{15t + 60} $ To get $15t + 60$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{4}{5t + 20} \times \dfrac{3}{3} = -\dfrac{12}{15t + 60} $ This give us: $ \dfrac{50}{15t + 60} = -\dfrac{75t - 75}{15t + 60} - \dfrac{12}{15t + 60} $ If we multiply both sides of the equation by $15t + 60$ , we get: $ 50 = -75t + 75 - 12$ $ 50 = -75t + 63$ $ -13 = -75t $ $ t = \dfrac{13}{75}$